An A Posteriori Analysis of C^0 Interior Penalty Methods for the Obstacle Problem of Clamped Kirchhoff Plates
This work provides a rigorous error analysis and adaptive algorithm for a class of finite element methods applied to a challenging fourth-order variational inequality, benefiting researchers in computational mechanics and numerical analysis.
The paper develops an a posteriori error analysis for C^0 interior penalty methods applied to the obstacle problem of clamped Kirchhoff plates, showing that a residual-based error estimator is both reliable and efficient. Numerical results demonstrate optimal performance of the adaptive algorithm for quadratic and cubic methods.
We develop an a posteriori analysis of C^0 interior penalty methods for the displacement obstacle problem of clamped Kirchhoff plates. We show that a residual based error estimator originally designed for C^0 interior penalty methods for the boundary value problem of clamped Kirchhoff plates can also be used for the obstacle problem. We obtain reliability and efficiency estimates for the error estimator and introduce an adaptive algorithm based on this error estimator. Numerical results indicate that the performance of the adaptive algorithm is optimal for both quadratic and cubic C^0 interior penalty methods.